I think Braids has an internal AD envelope. I never use it but you can configure it to drive the volume (vca) or tone of the oscillator. In any case, I would get a separate envelope generator to drive your Veils and to allow modulating stuff on the other modules.
Honestly: You need more modulation sources. Its way better to have a single oscillator with thee modulation sources than the other way around.
If you want to stay in the MI world:
Peaks is super versatile. It can be LFO, envelope, drums, random voltage source … and with the modified firmware it can be even more (bouncing ball simulator, turing machine, looping envelopes, etc, etc, etc). Only drawback is that you can’t modulate peaks’ parameters and that it can be difficult to remember what the knobs do in the various extra modes. Peaks has two independent (or not independent - as you whish) channels that can be in different modes, so you can have one channel play the ADSR and another be an LFO, etc.
Tides is very detailed and can be both envelope, VCO or LFO. However, it is AD/AR only, so if you stirctly need ADSR type envelopes, you’re out of luck. It is also not a dual channel module like peaks, but it offers to be modulated.
In your case I’d go for the Peaks first and move on from there. The million modes and dual channel nature (+ small footprint) make it ideal for small setups. Frankly, get two peaks. You can’t have enough of those.
And you might eventually want to add a shades to be able to mix and scale your modulation signals.